Dražen Adamović

A family of regular vertex operator algebras with two generators

AbstractFor every m ∈ ℂ ∖ {0, −2} and every nonnegative integer k we define the vertex operator (super)algebra Dm,k having two generators and rank

Lie Superalgebras and Irreducibility of \(A_1^{(1)}\) –Modules at the Critical Level

\frac{{3m}}{{m + 2}}

ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA

. If m is a positive integer then Dm,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that Dm,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.

\mathcal{W}(p)

Let D be the Lie algebra of regular differential operators on , and be the central extension of D. Let W 1+∞,minus;N be the vertex algebra associated to the irreducible vacuum -module with the central charge c = −N. We show that W 1+∞,−N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W 1+∞,−N -modules. Considering these modules as -modules, we identify the corresponding highest weights.

: A-SERIES

We introduce the infinite-dimensional Lie superalgebra

The Vertex Algebra

{\mathcal{A}}